In this article, the authors describe an algebra 2 class activity, called the Exponent Maze, that had students practice many mathematics problems, display their creativity, and work together collaboratively by creating their own mazes. The authors discuss how they introduced the activity, what the students created, and how creating mazes can be…

The study of loops and spaces in mathematics has been the subject of much interest among researchers. In Part 1 of "The Theory on Loops and Spaces," published in the "Mathematics Teaching Research Journal," introduced the concept and the basic underlying idea of this theory. This article continues the exploration of this topic…

This paper introduces the basic knowledge of integral factors of first-order ordinary differential equations and Lie symmetry analysis. It then discusses the principle of constructing an integral factor of the first-order ordinary differential equation by the Lie symmetric method. Finally, it presents some examples to show the process of…

In universities worldwide, there has been a movement away from mono-disciplinary towards multi-, inter- and transdisciplinary education, motivated by the notion that complex societal issues call for more than a single disciplinary perspective. To prepare students for a role in addressing these issues, flexibility within educational programs is…

Eddie Woo discusses the importance of problem solving in mathematics education. He points to the need for teachers to carefully consider the approaches they use to best support the growth of problem-solving abilities in students.

The notion of function is central in all of the secondary curriculum, and indeed functional models appear in almost all higher education that is based on mathematics. However, in secondary education, functions usually appear in restricted and somewhat sterile forms. In this (mostly theoretical) paper, we present a proposal -- exemplified by a…

The design of algorithms is one of the hardest topics of high school computer science. This is mainly due to the universality of algorithms as solution methods that guarantee the calculation of a correct solution for all potentially infinitely many instances of an algorithmic problem. The goal of this paper is to present a comprehensible and…

Building activities can be used any time in the school year in mathematics classes to promote problem solving, perseverance, and to develop students' spatial thinking. Spatial visualization skills are the "ability to mentally manipulate, rotate, twist, or invert a pictorially presented stimulus object." The authors were guided by the…

Four variations of the Koch curve are presented. In each case, the similarity dimension, area bounded by the fractal and its initiator, and volume of revolution about the initiator are calculated. A range of classroom exercises are proved to allow students to investigate the fractals further.

This paper suggests that artificial intelligence in education (AIEd) can be fruitfully analysed as 'policies frozen in silicon'. This means that they exist as both materialised and proposed problematisations (problem representations with corresponding solutions). As a theoretical and analytical response, this paper puts forward a heuristic lens…

This paper discusses the mathematical and didactical problems of teaching indefinite integral in the context of the ubiquitous availability of online integral calculators. The symbol of indefinite integral introduced by Leibniz, unfortunately, does not contain an indication of the interval on which the antiderivatives should be calculated. This…

What comes to mind when one thinks about building? One may envision constructions with blocks or engineering activities. Yet, constructing and building a number system requires the same sort of imagination, creativity, and perseverance as building a block city or engaging in engineering design. We know that children invent their own notation for…

In this article, the author presents a teaching prompt--Write-it-Out--to instruct readers who seemingly guess at words with no or limited use of grapheme-phonemic correspondences to recontextualize word-solving into writing. Through the nature of this prompt, slowing down the pace of solving words on the run with writing also reciprocally builds…

A very common Applied Optimization Problem in Calculus deals with minimizing a distance given certain constraints, using Calculus, the general method for solving these problems is to find a function formula for the distance that we need to minimize, take the derivative of the distance function, set it equal to zero, and solve for the input value,…

We will present a problem-solving method for the dynamics of a projectile that has two perpendicular acceleration vectors through rotation of the axes. This methodology of reparameterizing the two-dimensional system simplifies the speed optimization calculus.